The revival will star Scarlett Johansson as Maggie, the wife of an alcoholic ex-football player named Brick, according to The New York Times.
Pine and Renner are currently in contention for the role of Brick, though theatre executives told the publication that Pine is their top choice.
The revival is slated to premiere in spring 2013.
Johansson previously scored a Tony Award for her portrayal of a sheltered niece in A View From the Bridge.
Pine recently finished shooting the long-awaited follow-up to 2009's Star Trek. He will reprise his role as Captain James T Kirk in the sequel.
Johansson and Renner co-starred in The Avengers and are expected to reunite for a sequel.
Watch Chris Pine discuss his role in This Means War with Digital Spy below: